Method and apparatus for kidney function analysis

ABSTRACT

A method and apparatus for determining physiological data related to an animal, such as kidney diagnostics data, is provided. The method includes injecting a mixture of a first and a second molecule into an animal (e.g., a human patient), determining a molecular ratio of the molecules, and determining the physiological data based on the molecular ratio. The apparatus includes a number of finger receiving apertures, a light generation circuit, a light detection circuit, a pulse counting circuit, and a user interface.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a U.S. national counterpart application ofinternational application serial No. PCT/US2006/014576 filed Apr. 18,2006, which claims priority to U.S. Provisional Patent Application No.60/672,708, filed Apr. 19, 2005. The entireties of both of which arehereby incorporated by reference.

This patent application claims priority to and the benefit of U.S.Provisional Patent Application Ser. No. 60/672,708 entitled “Method andApparatus For Kidney Function Analysis,” which was filed on Apr. 19,2005, the entirety of which is expressly incorporated herein byreference.

BACKGROUND OF THE INVENTION

The present disclosure relates generally to methods and apparatuses fororgan diagnostics, and more particularly to methods and apparatuses forkidney diagnostics.

Measurement of kidney functions is an important step in the diagnosisand treatment of kidney diseases. One such measure of kidney function isthe Glomerular Filtration Rate (GFR). GFR is defined as the volume ofblood (blood plasma) filtered by the kidney within a given time and istypically measured in milliliters per minute (ml/min). The typicalclinical method used to measure GFR is the measurement of urinecreatinine clearance. Creatinine is a metabolic product of the body.However, the GFR estimated by measuring creatinine level in the urine isonly an estimate and not a direct measure of the actual GFR. This isbecause creatinine is produced by the body constantly and secreted intothe urine in addition to filtration. Typical GFR measurements take atleast 6 hours to 24 hours to complete. However, GFR measurements may notbe possible when serum creatinine levels are not in equilibrium such asduring acute renal failure. Typical GFR measurement techniques requirecollecting urine samples and/or drawing blood samples.

There are many diseases that affect the kidney or functions of thekidney. Proteinuria is a marker of chronic disease. An animal (e.g., ahuman patient) with proteinuria may develop renal failure, and earlydetection of proteinuria is beneficial in the treatment of manyunderlying diseases. The typical diagnostic method for proteinuria isthe measurement of the albumin level in the urine. Such measurement istypically done semi-quantitatively using urine dip sticks or bychemically measuring the urinary protein to creatine ratio. Quantitativeanalysis typically requires a 24-hour urine collection. However, even24-hour urine collection may result in a delayed diagnosis because ofprotein removal from the urine by proximal tubule cell reabsorption. Forexample, proteins may pass through the glomerulus (kidney filtrationbarrier), enter into the renal filtrate, and be reabsorbed by the renaltubular cells leaving little to no proteins in the urine. This may be ofparticular concern in diabetic nephropathy when the earliest detectionof an altered glomerular permeability to protein is crucial forinstitution of therapy.

Blood and urine glucose levels are also used as diagnostic measurement.Abnormal blood glucose levels are directly related to diabetes and otherdiseases. Typical methods used to determine blood and urine glucoselevels require the drawing of blood and/or the measurement of glucosecontent in the urine. These methods are relatively slow and do not allowreal time monitoring of blood glucose levels.

Further, in many applications, it is desirable to know thepharmacokinetics of a drug. Typical methods used to measure drugpharmacokinetics require the drawing of blood from an animal (e.g., ahuman patient) which can be painful and slow. Other methods used tomeasure drug pharmacokinetics include the use of heavy and expensivemedical imaging devices such as MRI.

SUMMARY OF THE INVENTION

The present invention comprises one or more of the features recited inthe appended claims and/or the following features which, alone or in anycombination, may comprise patentable subject matter:

A method for determining a physiological diagnostic of an animal isprovided. The method may include the step of injecting a mixture of anumber of first molecules and a number of second molecules into theanimal. The molecular weight of the second molecule may be greater thanthe first molecule. The first and second molecules may be fluorescentprobes. The method may also include the step of determining a molecularratio of the first molecules and the second molecules. The molecularratio may be a fluorescent intensity ratio of the first and secondmolecules. The method may further include determining physiologicaldata. The physiological data may be, for example, a plasma clearancerate constant of a drug or chemical compound, a glomerular filtrationrate, a filtration resistance, a clearance rate of glucose, a filtrationresistance value of glucose, a glucose metabolic rate, and/or a drugmetabolic rate. The glucose or drug metabolic rate may be determinedbased on the clearance rate of the glucose or drug and the filtrationresistance value of glucose or of the drug, respectively.

An apparatus for determining a physiological diagnostic of an animal isalso provided. The apparatus may include a number of finger receivingapertures. The apparatus may also include a number of light sources anda number of associated light receivers. Each of the number of lightsources and associated light receivers may be associated with one of thenumber of finger receiving apertures. The light sources may belight-emitting diodes, lasers, diode lasers, and/or white light sourcescoupled with wavelength selection optics. The apparatus may furtherinclude a light generation circuit coupled to the number of lightsources and a light detection circuit coupled to the number ofassociated light receivers. The light generation circuit may include adigital-to-analog converter circuit. The light detection circuit may beconfigured to detect a number of optical signals from the lightreceivers. The light detection circuit may also include a number ofamplifiers and/or a number of filters. The apparatus may additionallyinclude a photon pulse counting circuit. The photon pulse countingcircuit may use TTL for digital signal detection. The pulse countingcircuit may be coupled to the light detection circuit. The pulsecounting circuit may be configured to determine a physiologicaldiagnostic value based on the number of optical signals. Alternatively,in some embodiments, an analog-to-digital converter circuit may be usedand configured for analog signal detection. The apparatus may yetfurther include a user interface electrically coupled to the pulsecounting circuit. The user interface may include a display screen fordisplaying the physiological diagnostic value. The pulse countingcircuit (or an analog-to-digital converter circuit) may be wirelesslycommunicatively coupled to the light detection circuit. Further, thelight generation circuit, the pulse counting circuit, oranalog-to-digital converter circuit, and the user interface may formportions of a personal computer.

The above and other features of the present disclosure, which alone orin any combination may comprise patentable subject matter, will becomeapparent from the following description and the attached drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The detailed description particularly refers to the following figures,in which:

FIG. 1 is a process flow diagram of an algorithm for determining akidney diagnostic;

FIG. 2 is a process flow diagram of an embodiment of the algorithm ofFIG. 1 for determining a Glomerular Filtration Rate of a kidney;

FIG. 3 is a process flow diagram of an embodiment of the algorithm ofFIG. 1 for determining a protein filtration resistance;

FIG. 4 is a process flow diagram of an embodiment of the algorithm ofFIG. 1 for determining a blood glucose clearance rate and metabolicrate;

FIG. 5 is a process flow diagram of an embodiment of an algorithm fordetermining a Glomerular Filtration Rate of a kidney using a calculatedvolume of distribution;

FIG. 6 is a perspective view of a measurement head of an apparatus fordetermining physiological diagnostics;

FIG. 7 is a top plan view of the measurement head of FIG. 6;

FIG. 8 is a perspective view of an alternative embodiment of themeasurement head of FIG. 6; and

FIG. 9 is schematical illustration of a control unit of an apparatus fordetermining physiological diagnostics for use with the measurement headof FIG. 6 or FIG. 8.

DETAILED DESCRIPTION OF THE DRAWINGS

While the concepts of the present disclosure are susceptible to variousmodifications and alternative forms, specific exemplary embodimentsthereof have been shown by way of examples in the drawings and willherein be described in detail. It should be understood, however, thatthere is no intent to limit the concepts of the present disclosure tothe particular forms disclosed, but on the contrary, the intention is tocover all modifications, equivalents, and alternatives falling withinthe spirit and scope of the disclosure.

Referring to FIG. 1, an algorithm 10 for determining physiological data,such as kidney diagnostic data, is shown. The algorithm 10 may be usedto determine the Glomerular Filtration Rate of the kidneys, themolecular filtration resistance of a molecule and/or particle withpredetermined sizes, and other kidney diagnostic measurements. To do so,in process step 12, a mixture of two (or more) molecules, i.e. A & B (ormore), are injected into a live animal. As used herein, the term“animal” is intended to include humans. The two (or more) molecules areof different sizes (i.e., different molecular weight). Molecules withlarge molecular weights (MW) are typically retained in the blood streamfor a long period of time (hours to days) in animals (e.g., humanpatients) with relatively normal renal functions. If one of the two ormore molecules is of a large molecular weight (e.g. molecule A>70 kiloDalton), the filtration of the other molecule(s) (e.g., molecule B) canbe monitored and the clearance rate of molecule B can be calculatedbased thereon.

In process step 14, the molecular ratio of the molecules is determined.The molecular ratio (or generalized polarity (GP)) of B/A, R_(B/A),measured in the blood stream as a function of time is directly relatedto the relative filtration rates (clearance rates) of these molecules, A& B (or more). The signal that represents molecular ratio, R_(B/A),includes any properties that can be measured from A and B and may bedetermined based on the following equation:

$\begin{matrix}{R_{B/A} = \frac{S_{B}}{S_{A}}} & (1)\end{matrix}$

where, S_(A) is any one of a number of types of signals measured from Aand S_(B) is any one of a number of types of signals measured from B.The types of signals, S_(A) and S_(B), may include, but are not limitedto, fluorescent intensity, any scattering signal (Rayleigh scattering,Raman, coherent anti-stock scattering, etc) from incident light (at oneor more wavelengths), fraction of fluorescence lifetimes (in this case,the ratio signal R_(B/A) is a ratio between the fractional contributionof fluorescence lifetime from B and the fractional contribution offluorescence lifetime from A), absorbance, and polarization. This ratiosignal (between A and B or more) also includes any combinations betweenany types of signals from A and B, e.g. ratio between fluorescent signalfrom A and scattering signal from B. In addition, a ratio signal,R_(B/A)=S_(B), may be used when S_(A)=1 (a stationary signal of Anormalized to 1).

In process step 16, the kidney diagnostics of interest is determinedbased on the ratio of molecules. For example, the decay function ofR_(B/A)(t) (or GP(t)) after initial infusion of A, B (or more) mixturecan be described with a mathematical model (equation):

$\begin{matrix}{{R_{B/A}(t)} = {c + {\sum\limits_{i = 1}^{N}{a_{i}{\exp\left( {{- k_{i}}t} \right)}}}}} & (2)\end{matrix}$

where R_(B/A)(t) is the molecular ratio of molecules B and A measured asfunction of time; N is the total number of exponential processesinvolved including any glomerular filtration process, distributionprocess of the probe molecules in the blood stream, non-specific loss ofprobe molecules in the body, etc; c is a constant; a_(i) is apre-exponential factor or an amplitude; and k_(i) is the relative decayconstant (or rate constant) of individual processes, respectively. Theindividual values of k may be determined by performing linear (ornon-linear if desire) least square fitting of the time series R_(B/A)(t)(or GP(t)).

Where only the glomerular filtration process is present, the decayfunction R_(B/A)(t) is a single exponential:R _(B/A)(t)=c+aexp(−kt)  (3)

where R_(B/A)(t) is the molecular ratio of molecules B and A measured asfunction of time, c is a constant and a is the pre-exponential factor orthe amplitude and k is the relative decay constant (or rate constant).As described above, if molecule A has a large molecular weight (e.g.,greater than about 70 kD) and, therefore, is retained the kidney, theconcentration of the molecule A in the blood stream can be consideredstationary. By performing linear (or non-linear if desire) least squarefitting of the time series R_(B/A)(t) (or GP(t)), the value of k can bedetermined. The rate constant k (of the glomerular filtration process)is directly related to the glomerular filtration rate (GFR) and thetotal blood plasma volume, V_(plasma) and molecular resistance, ξ,according to the following relationship:

$\begin{matrix}{k = {\xi\frac{GFR}{V_{plasma}}}} & (4)\end{matrix}$

The value of molecular filtration resistance ξ, is a measure of howdifficult a molecule can pass through the kidney. If a molecule (orsubstance) has ξ=1, the molecule (or substance) can freely pass throughthe kidney filtration barrier without resistance. If a molecule (orsubstance) has ξ<1, the molecule (or substance) cannot freely passthrough the kidney filtration barrier. If a molecule (or substance) hasξ>1, the molecule (or substance) is actively passing through (due toexistence of active transportation mechanisms) the kidney filtrationbarrier.

The plasma volume, V_(plasma), is proportional to the body weight W_(b)and they have the following relationship:V _(plasma)=ρ(ηW _(b))  (5)

where η is a weight-whole blood (including both plasma and blood cells)volume factor and ρ is a percentage factor of blood plasma volume fromthe whole blood volume. Average values of ρ and η of human are known orcan be measured. In other embodiments, other methods of determining theplasma volume, V_(plasma), may be used. For example, V_(plasma) may bedetermined using any one or more of the determination procedures and/orequations discussed in detail below in regard to process step 60 ofalgorithm 50, which is illustrated in FIG. 5.

Accordingly, based on the molecular ratio as determined by equation 1described above, kidney GFR and molecular filtration resistance ξ, maybe determined for any molecules (or substances) using one or more of theequations 2-5 as described above.

In the following discussion of the decay constant k, molecularfiltration rate, clearance rate, and rate constant are usedsynonymously. The relative molecular separation between molecule A andmolecule B may be quantified using the Generalized Polarity based on thefollowing equation:

$\begin{matrix}{{GP} = \frac{I_{A{({large})}} - I_{B{({small})}}}{I_{A{({large})}} + I_{B{({small})}}}} & (6)\end{matrix}$

where I_(A(large)) is the signal from the larger molecule andI_(B(small)) is the signal from the smaller molecule. GP=1, when thereis only signal from the larger molecule (only molecule A is present),and GP=−1 when there is only signal from the smaller molecule (onlymolecule B is present).

Alternatively, GP can also be defined asGP=(I_(B(small))−I_(A(large)))/(I_(A(large))+I_(B(small))). For thepurpose of convention and discussion, the definition of GP in Equation 6is used, but other definitions of GP may be used in other embodiments.The GP value can be used for quantification of the relative strength(namely the polarity of relative occupation of molecule A and moleculeB) of the two individual signals from molecule A and B, respectively.

It should be appreciated that algorithm 10 may be used to determine anyone of a number of kidney diagnostics. For example, referring now toFIG. 2, an algorithm 20 for determining a Glomerular Filtration Rate ofa kidney is shown. Algorithm 20 includes process step 22 in which amixture of two fluorescent probes (A and B) dissolved in saline or otheraqueous solutions is injected into the blood stream of an animal. Thefluorescent probes are of different sizes. For example, one of thefluorescent probes (e.g., probe A) may have a molecular weight (WM) oflarger than 70 kD such as a 70 kD or a 500 kD fluorescent labeleddextran. The fluorescent signal from probe A is used as the referencesignal. The other fluorescent probe (probe B) has smaller molecularweight that is not metabolized in the body. For example, fluorescentprobe B may be small fluorescent molecules such as fluorescein, cascadeblue, fluorescently labeled inulin, or other none toxic compounds.

In process step 24, the fluorescence intensity ratio for the injectedprobes is determined. The fluorescence intensity ratio may be determinedaccording to the equation: R_(B/A)(t)=I_(B)(t)/I_(A)(t), where I_(B)(t)and I_(A)(t) are fluorescence intensities of the molecules B and Ameasured as functions of time, respectively. The fluorescence intensityratio is measured from the blood stream (blood vessel/vessels) as afunction of time after initial dye mixture injection. In process step26, the GFR is calculated using the above-described equations 1-5 andleast square fittings, assuming ξ for the smaller probe molecule isclose to unity (ξ=1).

Additionally, algorithm 10 may be used as a diagnostic measure forProteinuria. For example, referring to FIG. 3, an algorithm 30 fordetermining a protein filtration resistance as a diagnostic measurementfor Proteinuria is shown. Algorithm 30 includes a process step 32 inwhich a mixture of three fluorescent probes (A, B and C) dissolved insaline or other aqueous solutions is injected into the blood stream.Probes A and B are analogous to A and B described above in regard toalgorithm 20. Probe C is a fluorescently labeled protein (the markerprotein) of any kind (globular or non-globular proteins), for example, aTexas-Red or FITC (fluorescein isothiocyanate) conjugated albumin.

In process step 34, the fluorescent signals from probes A, B and C inthe blood vessels are recorded as functions of time. By performing leastsquare fit of the fluorescence intensity ratio,R_(B/A)(t)=I_(B)(t)/I_(A)(t), using the above-described equation 2 or 3,the rate constant k₁ of probe B may be determined. Similarly, by fittingthe intensity ratio, R_(C/A)(t)=I_(C)(t)/I_(A)(t), the rate constant k₂of C (the protein) can be determined. In process step 36, the filtrationresistance is determined. The relative filtration resistance ξ_(C/B) maybe calculated directly according to the following equation:

$\begin{matrix}{\xi_{C/B} = \frac{k_{2}}{k_{1}}} & (7)\end{matrix}$

If ξ_(B)=1, the relative filtration resistance ξ_(C/B)=ξ_(C) (filtrationresistance of the marker protein).

The filtration resistance may be used as an indicator of the difficultylevels of the marker protein to pass through the kidney filtrationbarrier. A smaller value of ξ_(C) indicates a greater difficulty levelfor the protein to pass through the kidney filtration barrier. Thisproperty of protein filtration resistance ξ can be used to diagnoseProteinuria. If an animal (e.g., a human patient) has a filtrationresistance (of the marker protein) value larger than the average proteinfiltration resistance value from healthy individualsξ_(patient)>ξ_(average), it is likely the animal has developedProteinuria.

In an alternative embodiment, the protein filtration resistance may bedetermined using two separate injections and associated measurements. Inthe first injection and measurement step, a mixture including onlyprobes A and B is injected and the rate constant k₁ is determinedthereafter. Subsequently, a mixture including only probes A and C isinjected and the rate constant k₂ is determined thereafter.

Additionally, algorithm 10 may be used as a diagnostic measure for bloodglucose. For example, referring to FIG. 4, an algorithm 40 fordetermining a blood glucose clearance rate and metabolic rate is shown.Algorithm 40 includes a process step 42 in which a mixture of threefluorescent probes (A, B and C1) dissolved in saline or other aqueoussolutions is injected to the blood stream. Probes A and B are analogousto A and B described above in regard to algorithm 20. Probe C1 is afluorescent glucose analog (L-glucose) where the glucose has a left-handchirality (Levo-glucose in latin). L-glucose is not sweet and notmetabolized by the body. In process step 44, the clearance rate k_(f)and the filtration resistance k_(f) of glucose (obtained from L-glucose)are determined. The clearance rate k_(f) and the filtration resistanceξ_(f) of glucose may be determined by using algorithm 30 described abovein regard to FIG. 3.

In process step 44, the glucose metabolic rate is determined. ForD-glucose (Dextro-glucose, having a right-hand chirality), the body willmetabolize this glucose as well as clear (filter) it from the blood. Ifa mixture of three fluorescent probes (A, B and C2) with C2 being afluorescent glucose analog, such as 2-NBDG[2-(N-(7-nitrobenz-2-oxa-1,3-diazol-4-yl)amino)-2-deoxyglucose] or6-NBDG, where the glucose has a right-hand chirality, the fluorescenceintensity ratio R_(C2/A)(t)=I_(C2)(t)/I_(A)(t) measured as function oftime can be determined based on the following equation:R _(C2/A)(t)=c+aexp(−k _(f) t)+M(k _(m) ,t)  (8)

where k_(f) is the glucose filtration rate solely due to filtration, andM(k_(m),t) is a function describing the kinetics of glucose metabolism,and k_(m) is the glucose metabolic rate. k_(f) is known from processstep 42, described above, using L-glucose fluorescent analog. Theglucose metabolic rate, k_(m), may be determined in process step 44 byfitting the glucose metabolic function M(k_(m),t).

Alternatively, the glucose metabolic rate may be determined by using asingle injection of fluorescent probe mixture (A, C1 and C2) with Abeing the larger fluorescent molecule (>70 kD dextran), C1 being theL-glucose fluorescent analog, and C2 being D-glucose fluorescent analog.The glucose metabolic function may then be determined based on thefollowing equation:

$\begin{matrix}{{M\left( {k_{m},t} \right)} = {{{R_{C\;{2/A}}(t)} - {R_{C\;{1/A}}(t)}} = \frac{{I_{C\; 2}(t)} - {I_{C\; 1}(t)}}{I_{A}(t)}}} & (9)\end{matrix}$

Further, algorithm 10 may be used to determine a drug clearance rateand/or metabolic rate. For example, the pharmacokinetics of metabolicand non-metabolic drugs may be monitored and measured using thealgorithm 30 described above in regard to FIG. 3. For non-metabolicdrugs (wherein only the clearance rate of the drug is considered), C1from the fluorescent probe mixture (A, B and C1) described above inregard to algorithm 30 is replaced with a drug compound in order tomeasure this drug's clearance rate k and filtration resistance ξ. For ametabolic drug, the algorithm 40 described above in regard to FIG. 4 maybe used by replacing the glucose with a respective drug compound todetermine its clearance rate and the metabolic rate.

It should be appreciated that the determination of the glomerularfiltration rate (GFR) of the kidneys, and the molecular filtrationresistance of a molecule if desired, may be improved by accounting fornon-renal clearance mechanisms (i.e., accounting for the non-renalclearance portion of k of equation 3 above). In addition, suchdeterminations may be improved by calculating the distribution volume,V_(D), of the animal (e.g., a human patient) being tested rather thanbasing the distribution volume on average values as discussed above inregard to equation 5. To do so, an algorithm 50 for determining aglomerular filtration rate of a kidney may be used as illustrated inFIG. 5.

The algorithm 50 begins with process step 52 in which a mixture of twofluorescent probes (A and B) dissolved in saline or other aqueoussolutions is injected into the blood stream of an animal. Thefluorescent probes are of different sizes. For example, one of thefluorescent probes (e.g., probe A) may have a molecular weight (WM) oflarger than 70 kD such as a 70 kD or a 500 kD fluorescent labeleddextran. The fluorescent signal from probe A is used as the referencesignal. The other fluorescent probe (probe B) has smaller molecularweight that is not metabolized in the body. For example, fluorescentprobe B may be small fluorescent molecules such as fluorescein, cascadeblue, fluorescently labeled inulin, or other none toxic compounds.

In process step 54, the fluorescence intensity ratio for the injectedprobes is determined. The fluorescence intensity ratio may be determinedaccording to the equation:R _(B/A)(t)=I _(B)(t)/I _(A)(t)  (10)

where I_(B)(t) and I_(A)(t) are fluorescence intensities of themolecules B and A measured as functions of time, respectively. Thefluorescence intensity ratio is measured from the blood stream (bloodvessel/vessels) as a function of time after initial dye mixtureinjection. The fluorescence intensity ratio may be determined using anysuitable imaging analysis apparatus. For example, in one particularembodiment, the apparatus 100 illustrated in and described below inregard to FIGS. 6-9 may be used.

Alternatively, in another embodiment, the intensity ratio may bedetermined by first generating microvascular images of the kidney usinga two-photon laser scanning fluorescence microscope system such as aMRC-1024P microscope, commercially available from Bio-Rad Laboratoriesof Hercules, Calif., equipped with a Nikon Diaphot inverted microscope,which is commercially available from Fryer Company Incorporated ofHuntley, Ill., and external detectors (e.g., a 440-470 nm, a 500-550 nm,and a 560-650 m detectors). Subsequently, the images may be analyzed todetermine the fluorescence intensity ratio using any suitable imaginganalysis system. For example, in one particular embodiment, the imagesmay be analyzed to determine the fluorescence intensity ratio using MetaImagining Series Version 6 software, which is commercially availablefrom Universal Imaging Corporation of West Chester, Pa. To do so, thethreshold level of each detection channel (i.e., each detector) may beset acceding to the average pixel value of an area of the image withoutsignificant autofluorescence from images taken before dye infusion. Theaverage pixel values of the intensity ratio, R, from a region ofinterest may then be exported into an data analysis and plotting programsuch as PSI-PLOT Version 6, which is commercially available from PolySoftware International of Pearl River, N.Y., for analysis.

Once the fluorescence intensity ratio has been determined, the overallplasma clearance rate is determined in process step 56. As discussedabove in regard to equation 3, when only the glomerular filtrationprocess is present, the decay function R_(B/A)(t) is a singleexponential time series. The overall plasma clearance rate may bedetermined by performing linear (or non-linear if desire) least squarefitting of this single exponential time series. For example, thefollowing decay function, R_(vessel)(t), may be used:R _(vessel)(t)=aexp(−k _(A) t)+c  (11)

where R_(vessel)(t) is the average pixel value of the intensity ratiofrom a given area (i.e., from a given blood vessel lumen region)extracted at different time points, a is the amplitude or thepre-exponential factor, c is a constant, t is time, and k_(A) is theoverall plasma clearance rate. As discussed above, the value of k_(A)may be determined by performing nonlinear least square fitting onequation 11.

It should be appreciated that the overall plasma clearance rate, k_(A),includes both the renal clearance rate, k_(A), and the non-renalclearance rate (e.g., take up by the liver), k_(A). As such, to improvethe accuracy of calculations based on the clearance rate, such asdetermining the glomerular filtration rate and/or the molecularfiltration resistance, the non-renal clearance rate may be subtractedfrom the overall plasma clearance rate or otherwise accounted for. To doso, the following equation may be used:k _(A) =k _(P) +k _(T) or  (12)k _(P) =k _(A) −k _(T)  (13)

wherein k_(A) is the overall plasma clearance rate, k_(P) is the rateconstant of the intrinsic plasma clearance (i.e., the renal clearance),and k_(T) is the non-specific tissue distribution rate constant of afreely filtered molecule (i.e., the non-renal clearance). As discussedabove, the value of k_(A) may be determined using equation 11 and, inembodiments wherein the animal upon which the kidney analysis procedureis being performed is a non-human animal, the value of the non-specifictissue distribution rate constant, k_(T), may be determined via a doublewhole kidney nephrectomy procedure. Because the value of the overallplasma clearance rate, k_(A), and the value of the non-specific tissuedistribution rate constant (i.e., the non-renal clearance rate), k_(T),are known, the value of the rate constant of the intrinsic plasmaclearance (i.e., the renal clearance rate), k_(P), may be determined viathe equation 13.

Alternatively, in embodiments wherein the animal upon which the kidneyanalysis procedure is being performed is a human patient, both the renaland non-renal clearance rates may be determined using multi-componentmodels to account for individual kinetic processes. For example, thefollowing equation may be used:R _(B/A)(t)=c+aexp(−k _(renal) t)+f(k _(non-renal) t)  (14)

wherein R_(B/A)(t) is the intensity ratio, a and c are constants, t istime, k_(renal) is the renal plasma clearance rate constant, f is afunction including all kinetic processes that are not part of renalclearance (e.g., probe distribution, non-specific tissue absorption,etc.), and k_(non-renal) is the non-renal plasma clearance rateconstant. The clearance rates, k_(renal) and k_(non-renal), may bedetermined by performing a multi-component least square fittingprocedure on equation 14. One of a number of different functions may beused to model the non-renal plasma clearance kinetics. For example, insome embodiments, a single exponential equation may be used as follows:f(k _(non-renal) t)=bexp(−k _(non-renal) t)  (15)

wherein b is a constant.

The accuracy of the determination of the renal and non-renal clearancerates may be improved by performing multiple tests on the human patientto determine multiple overall plasma clearance traces or values andsubsequently performing a least square fitting of the multiple overallplasma clearance traces (i.e., performing a global fitting procedure onequation 14). For example, multiple clearance values or traces can beobtained by performing a number of tests using various concentrationratios of the marker molecules (e.g., molecules A and B). The averagenon-renal clearance, k_(non-renal) may be then determined for an averagehuman patient statistically based on the multiple tests. Subsequently,the renal plasma clearance rate constant, k_(renal), may be determineddirectly using a single injection of the marker molecules (e.g.,molecules A and B) based on the following equation:k _(renal) =k _(overall) −k _(average non-renal)  (16)

wherein k_(renal) is the renal plasma clearance rate constant,k_(overall) is the average plasma clearance rate obtained by fitting themultiple clearance traces with a single exponential function, andk_(average) non-renal is the average non-renal clearance rate.

In process step 60, the volume of distribution, V_(D), is determined.Because at least one of the marker probes or molecules (e.g.,probe/molecule A) is relatively large (e.g., a 500 kD fluorescentlabeled dextran), this molecule or probe is not filtered by the kidney.As such, the volume of distribution, V_(D), may be expressed as followsaccording to the conservation principle:V _(D) =V _(before) *[C _(large)]_(before) /[C _(large)]_(plasma)  (17)

wherein V_(D) is the volume of distribution (i.e., the plasma volume),V_(before) is the volume of the large probe or molecule (e.g., the largedextran probe) before infusion into the patient, [C_(large)]_(before) isthe concentration of the large probe or molecule before infusion intothe patient, and [C_(large)]_(plasma) is the plasma concentration of thelarge probe or molecule after equilibrium has been obtained. Because thefluorescence intensity, I_(L), of the larger probe or molecule (e.g.,probe A) is proportional to its concentration, [C_(large)] the volume ofdistribution (i.e., the plasma volume), V_(D), may be determined asfollows:V _(D) =V _(before) *[I _(L)]_(before) /[I _(L)]_(plasma)  (18)

wherein V_(D) is the volume of distribution (i.e., the plasma volume),V_(before) is the volume of the large probe or molecule (e.g., the largedextran probe) before infusion into the patient, [I_(L)]_(before) is thetotal intensity values of the large probe or molecule measured beforeinfusion, and [I_(L)]_(plasma) is the total intensity values of thelarge probe or molecule measured after infusion. The value of volume ofthe large probe or molecule, V_(before), is known and the value of[I_(L)]_(plasma) may be determined from either the acquired time seriesimages or using fluorescence spectroscopy measurement of drawn bloodsamples taken after a predetermined time (e.g., 10 minutes) to allow theplasma concentration to stabilize. For example the value of[I_(L)]_(plasma) may be determined based on the average of three to fivetime, or more, time point measurements. The value of [I_(L)]_(before)may be determined using the same instrument settings as used todetermine the [I_(L)]_(plasma).

In some embodiments, the volume of distribution (i.e., the plasmavolume), V_(D), may be determined based on body weight of the animal(e.g., a human patient) rather than the use of the equation 18 providedabove. That is, the whole blood volume of the animal may be estimated as5.5% of the total body weight. The total plasma volume, V_(D), may thenbe estimated as 50% of the whole blood volume.

Although the process steps 56-60 are illustrated in FIG. 5 in asequential order, it should be appreciated that the renal clearance rateand the volume of distribution may be determined in any order withrespect to each other or contemporaneously with each other. For example,the volume of distribution may be determined prior to the determinationof the renal clearance rate in some embodiments. In other embodiments,the volume of distribution may be determined contemporaneously with thedetermination of the renal clearance rate.

Once the renal clearance rate k_(p) (or k_(Renal)) and that volume ofdistribution, V_(D), have been determined in process steps 58 and 60,respectively, the glomerular filtration rate (GFR) may be determined inprocess step 62 based thereon. To do so, the following equation may beused:GFR=k _(P) *V _(D)  (19)

wherein GFR is the glomerular filtration rate, k_(P) is the rateconstant of intrinsic plasma clearance (i.e., the renal clearance rate),and V_(D) is the volume of distribution. As discussed above, the valueof k_(P) may be determined using equations 12-13 or 14-16 and the valueof V_(D) may be determined using the equations 17-18 or estimated asdiscussed above in detail.

In addition to the glomerular filtration rate, in some embodiments, themolecular filtration resistance may also be determined in process step64. To do so, the following equation may be used.ξ=k _(Pf) /k _(P)  (20)

wherein ξ is the molecular filtration resistance, k_(Pf) is theintrinsic plasma clearance rate (i.e., the intrinsic plasma clearancerate of the kidney), and k_(P) is the plasma clearance rate of the largemolecule or probe (e.g., probe A). Because the large size moleculestypically do not freely pass through the glomerular filtration barrier,the clearance of the large size molecules from the blood will take alonger time than that of a freely filtered molecule. As such themolecular filtration rate can be used to determined the degree ofglomerular injuries by using large molecules of varying sizes. Becausemolecular filtration resistance of smaller molecules (e.g., thosemolecules of a size sufficient to be freely filtered though theglomerular filtration barrier) may be substantially similar in kidneyshaving minor and severe glomerular damage, the smaller molecules aretypically not used to determine the molecular filtration resistance.

In other embodiments, the molecular filtration resistance of the largemolecule (e.g., molecules>20 kD), ξ_(PLarge), may be determined usingthe following equation:ξ_(PLarge)=ξ_(FITC-inulin) *[k _(AP(FITC-inulin)) −k _(TP(FITC-inulin))]/[k _(APLarge) −k _(TPLarge)]  (21)

wherein ξ_(PLarge) is the molecular filtration resistance of the largemolecule (e.g., probe A), ξ_(FITC-inulin) is the filtration resistancevalue of FITC-inulin measured from a group of control animals,[k_(AP(FITC-inulin))−k_(TP(FITC-inulin))] is the plasma clearance rateof FITC-inulin measured from nephrosis animals at a given day after PANtreatment, and [k_(APLarge)−k_(TPLarge)] is the clearance rate constantof the large molecule of interest (e.g., probe A). It should beappreciated that the value of the molecular filtration resistance,ξ_(PLarge), may be compared with the corresponding values of measuredurinary protein-to-creatinine ratio to determine the correlation betweenξ_(PLarge) and urinary protein secretion and the sensitivity of usingthe ξ_(PLarge) value for early detection of proteinuria. It should beappreciated that in the above-described embodiment, FITC-inulin is usedas a GFR marker (e.g., as molecule/probe B). However, in otherembodiments, other types of GFR marker molecules/probes, such as otherfluorescent or non-fluorescent marker molecules, may be used. In suchembodiments, the equation 20 described above may be used to determinethe molecular filtration resistance.

After injection of fluorescent probe mixture according to any of theembodiments described above, measurements may be performed using amulti-photon laser scanning fluorescence microscope. The location ofmicroscopy measurements can be done any where on the body, for example,on the lips where the skin is relatively thin to allow easy observationof blood vessels. The fluorescence image of each of the injectedfluorescent probes is subsequently acquired. The average intensity valuefrom the blood vessel regions is calculated and plotted as functions oftime. These intensity time series of these fluorescent probes are usedfor fitting and retrieving the corresponding k, ξ and GFR.

However, other types of devices may be used to measure the fluorescenceintensity from the blood stream of the animal. For example, existinginstruments, such as instruments using optical coherent tomography orphoton migration (diffusion) principles, may be adapted to perform themeasurements.

Referring now to FIG. 6, one embodiment of an apparatus 100 fordetermining physiological data related to an animal is shown. Thephysiological data may be used for a number of analysis purposesincluding diagnostics purposes such as kidney diagnostics, testing, drugresearch, drug development, and the like. Apparatus 100 allowsnon-invasive measurement of kidney functions, as well as otherphysiological functions, using optical signals. Apparatus 100 includes ameasurement head 102 and a controller unit 120. The controller unit 120is illustrated and described below in regard to FIG. 9. The measurementhead 102 is illustratively designed to measure signals from the fingertips of human hands. However, in other embodiments, the measurement head102 may be configured to measure signals from other body parts of ahuman patient and/or animal including, for example, from toes, ears,wrist, etc.

The measurement head 102 includes a number of finger receivers 104designated as H1-H4. The finger receivers are configured to fit theanatomy of fingers from a human hand and may be embodied as cylindricalapertures. For example, as illustrated in FIG. 7, each of the fingerreceivers 104 extends at an angle, in respect to a vertical axis, tomatch the angle of the fingers of a human hand when the fingers areslightly separated. The measurement head 102 is made of a material thatrestricts ambient light from passing through the head 102. Themeasurement head 102 includes a number of source fiber optics, E1 a-E4a, coupled to a respective number of light sources, L1-L4, of thecontroller unit (see FIG. 9). The source fiber optics, E1 a-E4 a,deliver an illumination light to the palm side of the finger tips. Themeasurement head 102 includes a number of receiver fiber optics, E1-E4,that collect optical signals generated by the source fiber optics, E1a-E4 a. The receiver fiber optics, E1-E4, collect the optical signalsfrom the opposite side of the finger tips (i.e., the side with fingernail). The contacts between the fiber optics, E1 a-E4 a and E1-E4, andthe finger tips can be adjusted to assure good contact for illuminationand optical signal detection. This can be accomplished by directlyadjusting the fiber positions. In addition, the contact between thefiber optics and the finger nails can be improved by using anon-fluorescent coupling lubricant such as sucrose gel.

Referring now to FIG. 8, in an alternative embodiment, apparatus 100includes a measurement head 110 having a number of LEDs (light-emittingdiodes) 114, L1 a-L4 a, as light sources. The light sources, L1 a-L4 a,are in contact with, or near contact with, the palm side of the fingertips when the animal's (e.g., human patient's) fingers are inserted intothe finger receivers 112. Similar to measurement head 102, themeasurement head 110 includes a number of receiver fiber optics, E1-E4,to collect the optical signals generated from the finger tips byillumination (excitation) from the light sources, L1 a-L4 a,respectively. The receiver fiber optics are positioned on the oppositeside of the finger tips from the light sources (i.e., the side withfinger nail). The intensity of the LEDs may be controlled by thecontroller 120 through digital-to-analog converters (D/A converters).Because the light sources, L1 a-L4 a, are located in the measurementhead 110, loss of the illumination light is reduced.

The apparatus 100 also includes a controller unit 120. The controllerunit 120 determines the physiological diagnostic via photon counting.Photon counting is typically used in applications requiring sensitivesignal detection. In the illustrative embodiment, as illustrated in FIG.9, the controller unit 120 includes an optical portion 122 and a controlportion 124. In some embodiments, the optical portion 122 and thecontrol portion 124 are integrated into a single portable unit. In otherembodiments, optical portion 122 is integrated in a portable unit andthe control portion 124 is included in a personal computer. It should beappreciated that the control portion 124 may be included in the personalcomputer as separate hardware devices, separate software algorithms, ora combination of hardware devices and software algorithms.

In embodiments including a measurement head 102, the optical portion 122of the controller unit 120 includes a number of light sources 125,L1-L4, such as LEDs. The light sources 125 emit light at the same ordifferent wavelengths. Fiber optics are coupled to the LEDs that deliverlight to the measurement head 102. The optical portion 122 also includesa number of detectors 126, D1-D4. For the detection of fluorescence andother optical signals, the detectors may be embodied as photomultipliertubes, photodiodes, CCD, or other device capable of detecting thefluorescence and other optical signals. The optical signals aredelivered to the detectors through fiber optics that couple themeasurement head 102 to the controller unit 120. In addition, the opticportion 122 includes a number of optical filters 128, F1-F4. The opticalfilters 128 filter the optical signals by rejecting or filtering noiseand unwanted signals. The controller unit 120 also includes a number ofamplifiers 130, A1-A4, that amplify the analog signals received from thedetectors 126. The controller unit 120 includes a number ofdiscriminators 132, B1-B4, that discriminate single photon pulses andgenerate output singles therefrom. Illustratively, the output signalsare TTL (transistor-transistor logic) signals (so-called digitalsignal). However, it should be appreciated that in other embodiments,the discriminators 132 may generate other types of output signals.

The TTL signals generated by the discriminators 132 are transmitted tothe control portion 124 via a number of communication links 134. Thecommunication links 134 may be embodied as any type of communicationlink including discrete wires, PCB traces, or the like. Additionally, inother embodiments, the communication links 134 may be embodied aswireless communication links using any suitable wireless communicationprotocol such as, for example, Bluetooth. Once the output signals arereceived by the control portion 124, the output signals are processed bya pulse counting circuit 136 and further processed for display through auser interface 138 (e.g. a computer screen or a display panel on thecontroller unit). The control portion 124 also includesdigital-to-analog converters (DAC) 140. The DACs 140 may be used toadjust the voltage levels of the LEDs and thereby control theillumination intensity. It should be noted that in embodiments whereinmeasurement head 110 is used, the light sources, L1 a-L4 a, are locatedin the measurement head 110 rather than the optic portion 122. As such,the light sources, L1 a-L4 a, are coupled directly to the DAC block 140via a number of electrical interconnects, such as discrete wires. Itshould also be appreciated that although the illustrative embodimentincludes only four light sources or source fiber optics and associatedreceiver fiber optics, other embodiments may include any number of lightsources/source fiber optics and associated receiver fiber optics.

In an alternative embodiment, the digital signal acquisition andprocessing devices may be replaced with analog signal acquisition andprocessing devices. For example, the discriminators 132 may be removedor replaced with analog amplifiers and the pulse counting electroniccircuit 136 may be replaced with analog-to-digital conversion circuitry.It should also be appreciated that although the illustrative embodimentincludes only four light sources or source fiber optics and associatedreceiver fiber optics, other embodiments may include any number of lightsources/source fiber optics and associated receiver fiber optics.

The light sources, L1 a-L4 a and L1-L4, may be embodied as LEDs, diodelasers, Xenon, arc lamps with appropriate filters, or other type oflight source usable in the diagnostic measurement. The illuminationwavelength used is selected according to the available fluorescentprobes. For FITC-tagged molecules, an illumination at around 488 nm isused for the molecule excitation. A combination of blocking (blockingthe 488 nm excitation light) and bandpass filters that allow passingthrough 500-550 nm light may be placed in front of the correspondingdetector/detectors used for FITC fluorescence detection. In embodimentsusing scattering signal, the filter in front of the detector may allowthe illumination light to pass through. Examples of configurations forthe light sources, the filters, the fluorescent probes, and detectorsare provided below in table 1.

TABLE 1 Probes (fluorescent or Light Sources non-fluorescent)(wavelength) Filters (pass) Detectors Example 1 Cascade Blue-dextran L1(350-372 nm) F1 (400-460 nm) D1 (PMT) FITC-dextran L2 (465-490 nm) F2(500-550 nm) D2 (PMT) Texas Red-dextran L3 (594 nm) F3 (605-650 nm) D3(PMT) Cy5-dextran L4 (630-640 nm) F4 (655-700 nm) D4 (red sensitive PMT)Example 2 FITC-dextran L1 (465-490 nm) F1 (500-550 nm) D1 (PMT) TexasRed-dextran L2 (594 nm) F2 (605-650 nm) D2 (PMT) Cy5-dextran L3 (630-640nm) F3 (655-700 nm) D3 (red sensitive PMT) Scatter L4 (735 nm) F4(725-745 nm) D4 (red sensitive PMT) Example 3 FITC-dextran L1 (465-490nm) F1 (500-550 nm) D1 (PMT) Cy5-dextran L3 (632 nm) F3 (655-700 nm) D3(red sensitive PMT) Scatter L4 (632 nm) F4 (620-650 nm) D4 (redsensitive PMT)

Accordingly, it should be appreciated that the apparatus 100 may be usedin a number of applications for determining physiological diagnostics.For example, the apparatus 100 may be used to determine a glomerularfiltration rate (GFR) for diagnosis of kidney function, determine aprotein filtration resistance for diagnosis of Proteinuria and/or otherdiseases, determine a blood glucose clearance rate and/or glucosemetabolic rate, and/or determine a drug clearance rate and/or drugmetabolic rate. It should be appreciated that in some embodiments theapparatus 100 may include only one or a limited number of illuminationchannels and respective detection channels for a given application(e.g., GFR measurement using one fluorescent probe.).

While the disclosure has been illustrated and described in detail in thedrawings and foregoing description, such an illustration and descriptionis to be considered as exemplary and not restrictive in character, itbeing understood that only illustrative embodiments have been shown anddescribed and that all changes and modifications that come within thespirit of the disclosure are desired to be protected.

There are a plurality of advantages of the present disclosure arisingfrom the various features of the methods and apparatuses describedherein. It will be noted that alternative embodiments of the methods andapparatuses of the present disclosure may not include all of thefeatures described yet still benefit from at least some of theadvantages of such features. Those of ordinary skill in the art mayreadily devise their own implementations of the methods and apparatusesthat incorporate one or more of the features of the present inventionand fall within the spirit and scope of the present disclosure asdefined by the appended claims.

1. A method for determining the rate constant (k) of the clearance of afirst molecule and a second molecule by a kidney in an animal, themethod comprising: administering the first molecule and the secondmolecule to the animal, wherein the kidney clears the second moleculefrom the animal at a rate lower than the rate at which the kidney clearsthe first molecule from the animal; determining the molecular ratio(R_(B)/R_(A)) of the first molecule to the second molecule in the animalover a period of time to obtain a time series of molecular ratios(R_(B)/R_(A))_((t)), the molecular ratio (R_(B)/R_(A)) being determinedusing the following equation:R _(B) /R _(A) =I _(B) /I _(A), wherein I_(B) is the level of the firstmolecule in the animal and I_(A) is the level of the second molecule inthe animal; and determining the rate constant (k) from the time seriesof molecular ratios (R_(B)/R_(A))_((t)) using the equation:(R _(B) /R _(A))_((t)) =c+a*exp(−kt), wherein c is a constant, a is apre-exponential factor, and t is time.
 2. The method of claim 1, whereinthe level of the first molecule is determined based on the intensity ofa signal generated by the first molecule and the level of the secondmolecule is based on the intensity of a signal generated by the secondmolecule.
 3. The method of claim 2, wherein the signal generated by thefirst molecule is of a type different than the signal generated by thesecond molecule.
 4. The method of claim 2, wherein the signal generatedby the first molecule and the signal generated by the second moleculeare selected from the group consisting of fluorescence, a scatteringsignal from incident light, fraction of fluorescence lifetimes,absorbance, and polarization.
 5. The method of claim 1, wherein thefirst molecule and the second molecule are administered in a mixture. 6.The method of claim 1, wherein the molecular ratio (R_(B)/R_(A)) of thefirst molecule to the second molecule is replaced by the generalizedpolarity (GP) of the first molecule and the second molecule, thegeneralized polarity (GP) being determined using an equation selectedfrom the group consisting of:GP=(I _(A) −I _(B))/(I _(A) +I _(B))andGP=(I _(B) −I _(A))/(I _(A) +I _(B)) wherein I_(A) is the level of thesecond molecule in the blood and I_(B) is the level of the firstmolecule in the blood.
 7. The method of claim 1, further comprisingdetermining the glomerular filtration rate (GFR) of the kidney using thefollowing equation:GFR=(k*V _(plasma))/ξ wherein V_(plasma) is the plasma volume of theanimal, and ξ is the molecular filtration resistance of the firstmolecule.
 8. The method of claim 7, wherein the molecular filtrationresistance of the first molecule has a value of about
 1. 9. The methodof claim 2, wherein the second molecule is a fluorescent labeledmolecule having a molecule weight of greater than 70 kD.
 10. The methodof claim 2, wherein the second molecule has a molecular weight greaterthan the first molecule.
 11. The method of claim 1, wherein the animalis a human.
 12. A method for determining the rate constant (k₂) of theclearance of a first molecule and a second molecule by a kidney in ananimal, wherein the second molecule comprises a protein, the methodcomprising: administering the first molecule and the second molecule tothe animal; determining the molecular ratio (R_(B)/R_(A)) of the secondmolecule to the first molecule in the animal over a period of time toobtain a time series of molecular ratios (R_(B)/R_(A))_((t)), themolecular ratio (R_(B)/R_(A)) being determined using the followingequation:R _(B) /R _(A) =I _(B) /I _(A), wherein I_(B) is the level of the firstmolecule in the animal and I_(A) is the level of the second molecule inthe animal; and determining the rate constant (k₂) from the time seriesof molecular ratios (R_(B)/R_(A))_((t)) using the equation:(R _(B) /R _(A))_((t)) =c+a*exp(−k ₂ t), wherein c is a constant, a is apre-exponential factor, and t is time.
 13. The method of claim 12,wherein the method is used as a measure of proteinuria.
 14. The methodof claim 12, wherein the animal is a human.
 15. A method for determiningthe blood glucose clearance rate (k_(f)) of a kidney in an animal, themethod comprising: administering a first molecule and a second moleculeto the animal, wherein the second molecule comprises a glucose analogwhich is not metabolized; determining the molecular ratio (R_(B)/R_(A))of the second molecule to the first molecule in the animal over a periodof time to obtain a time series of molecular ratios (R_(B)/R_(A))_((t)),the molecular ratio (R_(B)/R_(A)) being determined using the followingequation:R _(B) /R _(A) =I _(B) /I _(A), wherein I_(B) is the level of the firstmolecule in the animal and I_(A) is the level of the second molecule inthe animal; and determining the blood glucose clearance rate (k_(f))from the time series of molecular ratios (R_(B)/R_(A))_((t)) using theequation:(R _(B) /R _(A))_((t)) =c+a*exp(−k _(f) t), wherein c is a constant, ais a pre-exponential factor, and t is time.
 16. The method of claim 15,wherein the glucose analog is L-glucose.
 17. The method of claim 15,wherein the animal is a human.
 18. A method for determining the glucosemetabolic function M(k_(m),t) of a kidney in an animal, the methodcomprising: administering a first molecule and a second molecule to theanimal, wherein the second molecule comprises a glucose analog which ismetabolized; determining the molecular ratio (R_(C2/A)) of the secondmolecule to the first molecule in the animal over a period of time toobtain a time series of molecular ratios (R_(C2)/R_(A))_((t)), themolecular ratio (R_(C2/A)) being determined using the followingequation:R _(C2/A) =I _(C2) /I _(A), wherein I_(B) is the level of the firstmolecule in the animal and I_(A) is the level of the second molecule inthe animal; and determining the glucose metabolic function M(k_(m),t)from the time series of molecular ratios (R_(B/A))_((t)) using theequation:(R _(C2/A))_((t)) =c+a*exp(−k _(f) t)+M(k _(m) ,t), wherein c is aconstant, a is a pre-exponential factor, and t is time.
 19. The methodof claim 18, wherein the glucose analog is D-glucose.
 20. The method ofclaim 18, wherein the animal is a human.